Adding, compounding and overlapping returns
Distinguish a sum of reported percentages from a linked same-account return, especially when event windows overlap.
Added 15 October 2026
Three calculations answer different questions
Adding percentages produces an arithmetic total of the listed values. Multiplying return factors produces a linked return for a compatible sequential series. Weighting account results by an appropriate capital base addresses another question. None is automatically the right interpretation of a marketing word such as aggregate. Write down the intended object before calculating. A label summarising several event results need not represent the change in one funded portfolio. Its original definition remains important even when the arithmetic itself is easy to reproduce.
Work a complete fictional chain
The teaching packet starts with an index of 100. Its invented segments return twenty percent, negative ten percent and five percent. Multiplication gives 100 times 1.20 times 0.90 times 1.05, ending at 113.4. The linked change is therefore 13.4 percent. Adding the three returns gives fifteen percentage points. The difference is not a rounding error: each segment in the chain acts on the previous balance. No account, broker or investment product generated these numbers; they were chosen to make the distinction inspectable.
An annual window can contain a quarter
An annual event and a quarter within that year may both be legitimate records while sharing performance time. Linking them as if one followed the other would count overlapping time twice. The same problem arises when a monthly record sits inside that quarter. Our worksheet sorts supplied segments by start date and reports gaps and overlaps. It withholds the linked output when the declared windows fail continuity. The arithmetic sum remains labelled a sum, not a replacement portfolio result or an implied combined investment.
The denominator must travel with the return
Two accounts can share dates and currency but have different deposits, withdrawals, leverage and calculation policies. Those differences matter before any capital-weighted combination. A trade-return sum does not disclose account weights or simultaneous exposure. A model catalogue can report useful per-model statistics without supplying a combined account path. Do not backsolve a portfolio curve from separate headline percentages. For this reason, the chain worksheet requires one account label and a declaration that segment returns already use a compatible cash-flow-adjusted basis.
Understand what the checker does not know
Input validation can reject duplicate segment IDs, malformed dates and overlapping intervals. It cannot establish that a declared account exists, that the return basis was applied properly or that all segments were supplied. Software tests reproduce arithmetic on controlled inputs; they are not independent trading observations. A passing chain therefore means the submitted labels and intervals satisfy the worksheet's rule. It does not mean the account was audited, the series was complete or the strategy is appropriate for a prospective investor.
Export assumptions as well as the answer
Keep the original input, sorted segment IDs, interval findings, arithmetic sum and linked result together. A zero denominator or an unlinked window should not disappear from a report because the final line looks inconvenient. The export retains null financial-validation fields and explicitly names its supplied-input scope. For a real performance analysis, obtain authentic statements and the governing calculation policy. This guide supplies a reproducible mathematical exercise, not a universal aggregation rule for competitions, fund composites, trade journals or historical product summaries.
An authored reading exercise
Try entering one invented segment from January 1 to April 1 and another from March 1 to April 1. Both can be individually valid observations, but they overlap. The chain worksheet retains both IDs, reports overlap and returns null for the linked result. Replacing the second start with April 1 changes the interval declaration; it does not establish that the underlying economic records are sequential. A real correction requires the actual source dates. This is why a mechanical date edit should never be used to rescue an attractive compounded headline.